MY CAR SEEMS LIKE IT IS NOT GETTING ENOUGH POWER WHEN I AM DRIVING IT, WHAT COULD IT BE?

2001 Chrysler PT Cruiser • 113,000 miles

It takes forever to get up speed. I have to push the gas all the way to the floor and keep it there awhile to get the car to go faster. During that time it the car sounds pretty loud. After all this happened I went to drive the car again and it wouldn't start at all. We tried to jump it off, let it charge for about 20 mins and it still won't crank. There is a brand new battery in it. Thinking its the alternator but it seems almost brand new. What could it be?